Investigations into analysis of hormone time series led to the development of a new technique and computer program named PULSEFIT. This model-based approach to characterizing circulating hormone measurements has been applied to measurement of LH in normal and orchiectomized males and in pre- and peripubertal males and females. We found that the most commonly used measure of pulsatility, namely number of pulses in the series, has a large statistical variability (50 to 100%). We defined a new pulsatility index which has considerably lower statistical variability and displays greater statistical power for discerning differences between groups within each of these studies. This new method provides better discrimination between the patterns of gonadotropin secretion during various stage of puberty than was previously appreciated. This method should be useful in the analysis and reanalysis of studies of pulsatile hormone secretion. We had previously developed a semiparametric approach to the analysis of families of curves, which combines the advantages of a parametric method (e.g., relative potency estimates) with the flexibility and versatility of nonparametric methods, such as smoothing cubic splines. However, the method was often slow to converge and sensitive to choice of initial estimates. Continuing theoretical studies of this method (FLEXIFIT) has led to a dramatic reduction in the size and complexity of the algorithm, accompanied by substantial increases in speed. The FLEXIFIT minimization algorithm is now comparable in speed to more routine, four-parameter logistic modeling. This enhancement comes at the cost of a negligible loss of optimality of the goodness of fit. However, the reduction of time and complexity promise to have a considerable impact on the practicality of the method. The FLEXIFIT method has been applied successfully to data from radioimmunoassays (RIA), bioassays, enzyme-linked immunosorbent assays (ELISA), and to the calibration curves which arise in polyacrylamide and agarose gel electrophoresis of proteins and nucleic acids.